R version 3.4.0 (2017-04-21)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Sierra 10.12.5

Matrix products: default
BLAS: /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] GAS_0.2.0

loaded via a namespace (and not attached):
 [1] pcaPP_1.9-61                Rcpp_0.12.11                compiler_3.4.0              nloptr_1.0.4               
 [5] ks_1.10.6                   xts_0.9-7                   tools_3.4.0                 bit_1.1-12                 
 [9] digest_0.6.12               jsonlite_1.5                lattice_0.20-35             ff_2.2-13                  
[13] Matrix_1.2-10               rugarch_1.3-6               shiny_1.0.3                 multicool_0.1-10           
[17] Bessel_0.5-5                parallel_3.4.0              mvtnorm_1.0-6               expm_0.999-2               
[21] knitr_1.16                  htmlwidgets_0.8             DistributionUtils_0.5-1     lmtest_0.9-35              
[25] grid_3.4.0                  R6_2.2.1                    rmgarch_1.3-0               rgl_0.98.1                 
[29] Rsolnp_1.16                 magrittr_1.5                codetools_0.2-15            htmltools_0.3.6            
[33] SkewHyperbolic_0.3-2        GeneralizedHyperbolic_0.8-1 MASS_7.3-47                 spd_2.0-1                  
[37] misc3d_0.8-4                mime_0.5                    xtable_1.8-2                httpuv_1.3.3               
[41] numDeriv_2016.8-1           sandwich_2.3-4              KernSmooth_2.23-15          truncnorm_1.0-7            
[45] FNN_1.1                     zoo_1.8-0                  


SECTION 3
---------

 
Table 1
        Label             Name                                                  Type          
norm    "\\code{norm}"    "Gaussian"                                            "univariate"  
snorm   "\\code{snorm}"   "Skew-Gaussian"                                       "univariate"  
std     "\\code{std}"     "Student-t"                                           "univariate"  
sstd    "\\code{sstd}"    "Skew-Student-t"                                      "univariate"  
ast     "\\code{ast}"     "Asymmetric Student-t with two tail decay parameters" "univariate"  
ast1    "\\code{ast1}"    "Asymmetric Student-t with one tail decay parameter"  "univariate"  
ald     "\\code{ald}"     "Asymmetric Laplace Distribution"                     "univariate"  
poi     "\\code{poi}"     "Poisson"                                             "univariate"  
ber     "%\\code{ber}"    "Bernoulli"                                           "univariate"  
gamma   "\\code{gamma}"   "Gamma"                                               "univariate"  
exp     "\\code{exp}"     "Exponential"                                         "univariate"  
beta    "\\code{beta}"    "Beta"                                                "univariate"  
negbin  "\\code{negbin}"  "Negative Binomial"                                   "univariate"  
skellam "\\code{skellam}" "Skellam"                                             "univariate"  
mvnorm  "\\code{mvnorm}"  "Multivariate Gaussian"                               "multivariate"
mvt     "\\code{mvt}"     "Multivariate Student-t"                              "multivariate"
        Parameters                                         N. of Parameters Scaling Type                         
norm    "\\code{location, scale}"                          "2"              "\\code{Identity, Inv, InvSqrt} \\\\"
snorm   "\\code{location, scale, skewness}"                "3"              "\\code{Identity} \\\\"              
std     "\\code{location, scale, shape}"                   "3"              "\\code{Identity, Inv, InvSqrt} \\\\"
sstd    "\\code{location, scale, skewness, shape}"         "4"              "\\code{Identity} \\\\"              
ast     "\\code{location, scale, skewness, shape, shape2}" "5"              "\\code{Identity, Inv, InvSqrt} \\\\"
ast1    "\\code{location, scale, skewness, shape}"         "4"              "\\code{Identity, Inv, InvSqrt} \\\\"
ald     "\\code{location, scale, skewness}"                "3"              "\\code{Identity, Inv, InvSqrt} \\\\"
poi     "\\code{location}"                                 "1"              "\\code{Identity, Inv, InvSqrt} \\\\"
ber     "\\code{location}"                                 "1"              "\\code{Identity, Inv, InvSqrt} \\\\"
gamma   "\\code{scale, shape}"                             "2"              "\\code{Identity, Inv, InvSqrt} \\\\"
exp     "\\code{location}"                                 "1"              "\\code{Identity, Inv, InvSqrt} \\\\"
beta    "\\code{scale, shape}"                             "2"              "\\code{Identity, Inv, InvSqrt} \\\\"
negbin  "\\code{location, scale}"                          "2"              "\\code{Identity, Inv, InvSqrt} \\\\"
skellam "\\code{location, scale}"                          "2"              "\\code{Identity} \\\\"              
mvnorm  "\\code{location, scale, correlation}"             "9"              "\\code{Identity} \\\\"              
mvt     "\\code{location, scale, correlation, shape}"      "10"             "\\code{Identity} \\\\"              


SECTION 4
---------



UNIVARIATE FORECAST
-------------------



Rolling forecast with univariate GAS



GAS rolling estimation asset 1 
GAS parameters mean
location    scale skewness    shape 
 0.05682  2.28883  1.10576  7.95181 
GAS parameters std
location    scale skewness    shape 
 0.01042  0.97537  0.02333  0.73440 
GAS parameters head
    location scale skewness shape
T+1  0.07702 1.635    1.083 6.777
T+2  0.07702 1.594    1.083 6.777
T+3  0.07702 1.577    1.083 6.777
T+4  0.07702 1.538    1.083 6.777
T+5  0.07702 1.518    1.083 6.777
T+6  0.07702 1.625    1.083 6.777
GAS parameters tail
      location scale skewness shape
T+95   0.04828 5.710    1.053 7.339
T+96   0.04828 5.592    1.053 7.339
T+97   0.04828 5.436    1.053 7.339
T+98   0.04828 5.356    1.053 7.339
T+99   0.04828 5.560    1.053 7.339
T+100  0.04828 5.394    1.053 7.339


GAS rolling estimation asset 2 
GAS parameters mean
location    scale skewness    shape 
 0.09148  2.16225  1.09106  8.45367 
GAS parameters std
location    scale skewness    shape 
 0.01953  1.15054  0.01240  1.27186 
GAS parameters head
    location scale skewness shape
T+1  0.07824 1.963    1.072 6.211
T+2  0.07824 1.875    1.072 6.211
T+3  0.07824 1.912    1.072 6.211
T+4  0.07824 1.877    1.072 6.211
T+5  0.07824 1.848    1.072 6.211
T+6  0.07824 1.825    1.072 6.211
GAS parameters tail
      location scale skewness shape
T+95   0.05213 5.331    1.092  8.88
T+96   0.05213 5.706    1.092  8.88
T+97   0.05213 5.829    1.092  8.88
T+98   0.05213 5.985    1.092  8.88
T+99   0.05213 5.757    1.092  8.88
T+100  0.05213 5.562    1.092  8.88


GAS rolling estimation asset 3 
GAS parameters mean
location    scale skewness    shape 
 0.06568  2.00681  1.04949  5.70312 
GAS parameters std
location    scale skewness    shape 
 0.01650  0.61647  0.01364  0.44013 
GAS parameters head
    location scale skewness shape
T+1  0.06532 1.672    1.082 5.759
T+2  0.06532 1.742    1.082 5.759
T+3  0.06532 2.000    1.082 5.759
T+4  0.06532 1.874    1.082 5.759
T+5  0.06532 1.882    1.082 5.759
T+6  0.06532 1.769    1.082 5.759
GAS parameters tail
      location scale skewness shape
T+95   0.07564 3.068    1.018 6.646
T+96   0.07564 2.953    1.018 6.646
T+97   0.07564 2.840    1.018 6.646
T+98   0.07564 3.130    1.018 6.646
T+99   0.07564 3.204    1.018 6.646
T+100  0.07564 3.272    1.018 6.646


GAS rolling estimation asset 4 
GAS parameters mean
location    scale skewness    shape 
  0.1054   2.0633   1.0207   7.7925 
GAS parameters std
location    scale skewness    shape 
 0.02277  1.69980  0.03060  1.08471 
GAS parameters head
    location scale skewness shape
T+1   0.1253 1.849    1.078 5.466
T+2   0.1253 1.788    1.078 5.466
T+3   0.1253 1.692    1.078 5.466
T+4   0.1253 1.606    1.078 5.466
T+5   0.1253 1.696    1.078 5.466
T+6   0.1253 1.808    1.078 5.466
GAS parameters tail
      location scale skewness shape
T+95   0.05766 13.15    1.024 7.029
T+96   0.05766 12.86    1.024 7.029
T+97   0.05766 13.04    1.024 7.029
T+98   0.05766 12.81    1.024 7.029
T+99   0.05766 12.26    1.024 7.029
T+100  0.05766 12.15    1.024 7.029


GAS rolling estimation asset 5 
GAS parameters mean
location    scale skewness    shape 
   0.105    2.293    1.068    7.424 
GAS parameters std
location    scale skewness    shape 
 0.03755  1.83432  0.01547  0.89571 
GAS parameters head
    location scale skewness shape
T+1    0.124 2.743    1.084 5.886
T+2    0.124 2.913    1.084 5.886
T+3    0.124 2.976    1.084 5.886
T+4    0.124 2.769    1.084 5.886
T+5    0.124 2.651    1.084 5.886
T+6    0.124 2.584    1.084 5.886
GAS parameters tail
      location scale skewness shape
T+95   0.03584 13.86    1.055 7.562
T+96   0.03584 13.47    1.055 7.562
T+97   0.03584 13.93    1.055 7.562
T+98   0.03584 13.57    1.055 7.562
T+99   0.03584 13.38    1.055 7.562
T+100  0.03584 12.87    1.055 7.562


GAS rolling estimation asset 6 
GAS parameters mean
location    scale skewness    shape 
 0.09422  2.09866  1.09098  5.80460 
GAS parameters std
location    scale skewness    shape 
 0.01293  0.61583  0.02106  0.65734 
GAS parameters head
    location scale skewness shape
T+1  0.07526 1.628    1.087 4.759
T+2  0.07526 1.601    1.087 4.759
T+3  0.07526 1.674    1.087 4.759
T+4  0.07526 1.625    1.087 4.759
T+5  0.07526 1.635    1.087 4.759
T+6  0.07526 1.574    1.087 4.759
GAS parameters tail
      location scale skewness shape
T+95    0.1003 4.607    1.047 5.996
T+96    0.1003 4.531    1.047 5.996
T+97    0.1003 4.477    1.047 5.996
T+98    0.1003 4.477    1.047 5.996
T+99    0.1003 4.463    1.047 5.996
T+100   0.1003 4.406    1.047 5.996


GAS rolling estimation asset 7 
GAS parameters mean
location    scale skewness    shape 
  0.0652   1.5806   1.0400  10.6887 
GAS parameters std
location    scale skewness    shape 
0.007583 0.531519 0.021117 2.775116 
GAS parameters head
    location scale skewness shape
T+1  0.06644 1.736     1.03 6.308
T+2  0.06644 1.692     1.03 6.308
T+3  0.06644 1.635     1.03 6.308
T+4  0.06644 1.648     1.03 6.308
T+5  0.06644 1.602     1.03 6.308
T+6  0.06644 1.629     1.03 6.308
GAS parameters tail
      location scale skewness shape
T+95   0.07572 2.361   0.9814 14.83
T+96   0.07572 2.277   0.9814 14.83
T+97   0.07572 2.267   0.9814 14.83
T+98   0.07572 2.460   0.9814 14.83
T+99   0.07572 2.352   0.9814 14.83
T+100  0.07572 2.253   0.9814 14.83


GAS rolling estimation asset 8 
GAS parameters mean
location    scale skewness    shape 
 0.06234  1.82425  1.08437  7.54023 
GAS parameters std
location    scale skewness    shape 
 0.01040  0.71331  0.01707  0.56113 
GAS parameters head
    location scale skewness shape
T+1  0.07305 1.852    1.067 6.437
T+2  0.07305 1.931    1.067 6.437
T+3  0.07305 1.926    1.067 6.437
T+4  0.07305 1.880    1.067 6.437
T+5  0.07305 1.835    1.067 6.437
T+6  0.07305 1.767    1.067 6.437
GAS parameters tail
      location scale skewness shape
T+95   0.04223 4.284     1.11 7.009
T+96   0.04223 4.177     1.11 7.009
T+97   0.04223 4.292     1.11 7.009
T+98   0.04223 4.309     1.11 7.009
T+99   0.04223 4.304     1.11 7.009
T+100  0.04223 4.206     1.11 7.009


GAS rolling estimation asset 9 
GAS parameters mean
location    scale skewness    shape 
 0.05925  1.98430  1.06676  6.41407 
GAS parameters std
location    scale skewness    shape 
 0.01642  0.79080  0.01280  0.31849 
GAS parameters head
    location scale skewness shape
T+1  0.08991 1.499    1.083 6.611
T+2  0.08991 1.474    1.083 6.611
T+3  0.08991 1.453    1.083 6.611
T+4  0.08991 1.533    1.083 6.611
T+5  0.08991 1.517    1.083 6.611
T+6  0.08991 1.492    1.083 6.611
GAS parameters tail
      location scale skewness shape
T+95   0.03401 4.007     1.06 6.284
T+96   0.03401 3.939     1.06 6.284
T+97   0.03401 4.014     1.06 6.284
T+98   0.03401 4.108     1.06 6.284
T+99   0.03401 4.074     1.06 6.284
T+100  0.03401 4.023     1.06 6.284


GAS rolling estimation asset 10 
GAS parameters mean
location    scale skewness    shape 
 0.08623  1.73649  1.07165 10.24144 
GAS parameters std
location    scale skewness    shape 
 0.02348  0.86480  0.01496  1.45779 
GAS parameters head
    location scale skewness shape
T+1  0.09247 1.430    1.054 9.242
T+2  0.09247 1.452    1.054 9.242
T+3  0.09247 1.508    1.054 9.242
T+4  0.09247 1.480    1.054 9.242
T+5  0.09247 1.448    1.054 9.242
T+6  0.09247 1.408    1.054 9.242
GAS parameters tail
      location scale skewness shape
T+95   0.03044 5.154    1.091 7.609
T+96   0.03044 5.173    1.091 7.609
T+97   0.03044 5.119    1.091 7.609
T+98   0.03044 5.217    1.091 7.609
T+99   0.03044 5.235    1.091 7.609
T+100  0.03044 5.227    1.091 7.609


GAS rolling estimation asset 11 
GAS parameters mean
location    scale skewness    shape 
 0.04779  2.39259  1.11526  7.71946 
GAS parameters std
location    scale skewness    shape 
 0.01269  1.33066  0.01499  1.37285 
GAS parameters head
    location scale skewness shape
T+1  0.05842 1.648    1.114 6.384
T+2  0.05842 1.862    1.114 6.384
T+3  0.05842 1.802    1.114 6.384
T+4  0.05842 1.792    1.114 6.384
T+5  0.05842 1.749    1.114 6.384
T+6  0.05842 1.720    1.114 6.384
GAS parameters tail
      location scale skewness shape
T+95   0.02103 6.545     1.09 5.667
T+96   0.02103 6.183     1.09 5.667
T+97   0.02103 5.904     1.09 5.667
T+98   0.02103 6.145     1.09 5.667
T+99   0.02103 6.148     1.09 5.667
T+100  0.02103 6.001     1.09 5.667


GAS rolling estimation asset 12 
GAS parameters mean
location    scale skewness    shape 
  0.1087   2.1357   1.0601   7.0112 
GAS parameters std
location    scale skewness    shape 
 0.03628  0.81834  0.01830  0.76781 
GAS parameters head
    location scale skewness shape
T+1   0.1411 1.979    1.043 7.382
T+2   0.1411 1.932    1.043 7.382
T+3   0.1411 1.890    1.043 7.382
T+4   0.1411 1.850    1.043 7.382
T+5   0.1411 1.788    1.043 7.382
T+6   0.1411 1.728    1.043 7.382
GAS parameters tail
      location scale skewness shape
T+95   0.02755 3.474    1.085 6.626
T+96   0.02755 3.462    1.085 6.626
T+97   0.02755 3.523    1.085 6.626
T+98   0.02755 3.659    1.085 6.626
T+99   0.02755 3.597    1.085 6.626
T+100  0.02755 3.474    1.085 6.626


GAS rolling estimation asset 13 
GAS parameters mean
location    scale skewness    shape 
 0.09137  2.50269  1.04423  5.52625 
GAS parameters std
location    scale skewness    shape 
 0.01338  0.93302  0.01129  0.38343 
GAS parameters head
    location scale skewness shape
T+1  0.07839 2.504    1.025 5.741
T+2  0.07839 2.428    1.025 5.741
T+3  0.07839 2.383    1.025 5.741
T+4  0.07839 2.311    1.025 5.741
T+5  0.07839 2.423    1.025 5.741
T+6  0.07839 2.337    1.025 5.741
GAS parameters tail
      location scale skewness shape
T+95   0.09102 3.363    1.033 5.151
T+96   0.09102 3.282    1.033 5.151
T+97   0.09102 3.364    1.033 5.151
T+98   0.09102 3.458    1.033 5.151
T+99   0.09102 3.503    1.033 5.151
T+100  0.09102 3.408    1.033 5.151


GAS rolling estimation asset 14 
GAS parameters mean
location    scale skewness    shape 
 0.06493  1.86806  1.06850  5.05205 
GAS parameters std
location    scale skewness    shape 
 0.02388  0.73201  0.01805  0.33244 
GAS parameters head
    location scale skewness shape
T+1  0.03424 2.108    1.063 4.911
T+2  0.03424 2.023    1.063 4.911
T+3  0.03424 1.949    1.063 4.911
T+4  0.03424 1.893    1.063 4.911
T+5  0.03424 1.879    1.063 4.911
T+6  0.03424 1.838    1.063 4.911
GAS parameters tail
      location scale skewness shape
T+95   0.04351 3.017    1.036 5.795
T+96   0.04351 2.917    1.036 5.795
T+97   0.04351 2.981    1.036 5.795
T+98   0.04351 2.986    1.036 5.795
T+99   0.04351 2.903    1.036 5.795
T+100  0.04351 2.818    1.036 5.795


GAS rolling estimation asset 15 
GAS parameters mean
location    scale skewness    shape 
  0.1441   2.6197   1.0301   7.3472 
GAS parameters std
location    scale skewness    shape 
 0.05465  0.95800  0.01138  0.46246 
GAS parameters head
    location scale skewness shape
T+1   0.2022 2.528    1.018 6.688
T+2   0.2022 2.439    1.018 6.688
T+3   0.2022 2.429    1.018 6.688
T+4   0.2022 2.508    1.018 6.688
T+5   0.2022 2.470    1.018 6.688
T+6   0.2022 2.397    1.018 6.688
GAS parameters tail
      location scale skewness shape
T+95   0.04479 3.976    1.008 7.184
T+96   0.04479 3.959    1.008 7.184
T+97   0.04479 3.877    1.008 7.184
T+98   0.04479 3.953    1.008 7.184
T+99   0.04479 3.962    1.008 7.184
T+100  0.04479 4.073    1.008 7.184


GAS rolling estimation asset 16 
GAS parameters mean
location    scale skewness    shape 
 0.07944  1.37482  1.06388  8.13495 
GAS parameters std
location    scale skewness    shape 
 0.02703  0.52150  0.01404  1.12006 
GAS parameters head
    location scale skewness shape
T+1   0.1035 1.753    1.045 7.413
T+2   0.1035 1.774    1.045 7.413
T+3   0.1035 1.913    1.045 7.413
T+4   0.1035 1.840    1.045 7.413
T+5   0.1035 1.896    1.045 7.413
T+6   0.1035 1.841    1.045 7.413
GAS parameters tail
      location scale skewness shape
T+95   0.03574 1.604    1.073 6.096
T+96   0.03574 1.630    1.073 6.096
T+97   0.03574 1.655    1.073 6.096
T+98   0.03574 1.605    1.073 6.096
T+99   0.03574 1.587    1.073 6.096
T+100  0.03574 1.532    1.073 6.096


GAS rolling estimation asset 17 
GAS parameters mean
location    scale skewness    shape 
 0.09076  2.29413  1.05768  7.55407 
GAS parameters std
location    scale skewness    shape 
 0.01825  1.37702  0.01493  0.83221 
GAS parameters head
    location scale skewness shape
T+1  0.08435 1.906    1.041 5.518
T+2  0.08435 1.821    1.041 5.518
T+3  0.08435 1.862    1.041 5.518
T+4  0.08435 1.820    1.041 5.518
T+5  0.08435 2.023    1.041 5.518
T+6  0.08435 2.137    1.041 5.518
GAS parameters tail
      location scale skewness shape
T+95   0.05816 8.067    1.087 6.933
T+96   0.05816 7.801    1.087 6.933
T+97   0.05816 8.044    1.087 6.933
T+98   0.05816 8.216    1.087 6.933
T+99   0.05816 7.902    1.087 6.933
T+100  0.05816 7.602    1.087 6.933


GAS rolling estimation asset 18 
GAS parameters mean
location    scale skewness    shape 
 0.07829  2.14360  1.08452  8.98147 
GAS parameters std
location    scale skewness    shape 
 0.01819  2.22697  0.01292  7.39820 
GAS parameters head
    location scale skewness shape
T+1  0.08375 1.379    1.066 6.904
T+2  0.08375 1.335    1.066 6.904
T+3  0.08375 1.342    1.066 6.904
T+4  0.08375 1.322    1.066 6.904
T+5  0.08375 1.410    1.066 6.904
T+6  0.08375 1.365    1.066 6.904
GAS parameters tail
      location scale skewness shape
T+95    0.0307 6.361    1.068 5.752
T+96    0.0307 6.527    1.068 5.752
T+97    0.0307 6.363    1.068 5.752
T+98    0.0307 6.931    1.068 5.752
T+99    0.0307 6.467    1.068 5.752
T+100   0.0307 6.272    1.068 5.752


GAS rolling estimation asset 19 
GAS parameters mean
location    scale skewness    shape 
 0.07524  1.46889  1.08443  7.56168 
GAS parameters std
location    scale skewness    shape 
 0.03464  0.62025  0.01407  1.09003 
GAS parameters head
    location scale skewness shape
T+1    0.128 1.522    1.077 7.505
T+2    0.128 1.599    1.077 7.505
T+3    0.128 1.607    1.077 7.505
T+4    0.128 1.568    1.077 7.505
T+5    0.128 1.521    1.077 7.505
T+6    0.128 1.490    1.077 7.505
GAS parameters tail
      location scale skewness shape
T+95   0.01631 2.311    1.086 5.913
T+96   0.01631 2.255    1.086 5.913
T+97   0.01631 2.220    1.086 5.913
T+98   0.01631 2.164    1.086 5.913
T+99   0.01631 2.179    1.086 5.913
T+100  0.01631 2.142    1.086 5.913


GAS rolling estimation asset 20 
GAS parameters mean
location    scale skewness    shape 
 0.05935  1.71363  1.06681  7.02748 
GAS parameters std
location    scale skewness    shape 
 0.01357  0.45880  0.02453  0.91478 
GAS parameters head
    location scale skewness shape
T+1  0.07053 1.733     1.06 8.014
T+2  0.07053 1.737     1.06 8.014
T+3  0.07053 1.754     1.06 8.014
T+4  0.07053 1.697     1.06 8.014
T+5  0.07053 1.645     1.06 8.014
T+6  0.07053 1.605     1.06 8.014
GAS parameters tail
      location scale skewness shape
T+95   0.06506 2.342    1.043 6.247
T+96   0.06506 2.273    1.043 6.247
T+97   0.06506 2.231    1.043 6.247
T+98   0.06506 2.231    1.043 6.247
T+99   0.06506 2.166    1.043 6.247
T+100  0.06506 2.104    1.043 6.247


GAS rolling estimation asset 21 
GAS parameters mean
location    scale skewness    shape 
 0.06296  1.57810  1.06965  5.08061 
GAS parameters std
location    scale skewness    shape 
0.007813 0.527023 0.017904 0.328835 
GAS parameters head
    location scale skewness shape
T+1  0.07356 1.581    1.043 4.904
T+2  0.07356 1.659    1.043 4.904
T+3  0.07356 1.689    1.043 4.904
T+4  0.07356 1.680    1.043 4.904
T+5  0.07356 1.647    1.043 4.904
T+6  0.07356 1.640    1.043 4.904
GAS parameters tail
      location scale skewness shape
T+95   0.05202 2.860    1.073 4.912
T+96   0.05202 2.801    1.073 4.912
T+97   0.05202 2.819    1.073 4.912
T+98   0.05202 2.807    1.073 4.912
T+99   0.05202 2.975    1.073 4.912
T+100  0.05202 3.185    1.073 4.912


GAS rolling estimation asset 22 
GAS parameters mean
location    scale skewness    shape 
 0.07969  1.77457  1.05684  6.52023 
GAS parameters std
location    scale skewness    shape 
 0.03341  0.53282  0.05166  1.22483 
GAS parameters head
    location scale skewness shape
T+1   0.1185 2.034    1.104 7.729
T+2   0.1185 2.147    1.104 7.729
T+3   0.1185 2.228    1.104 7.729
T+4   0.1185 2.210    1.104 7.729
T+5   0.1185 2.121    1.104 7.729
T+6   0.1185 2.135    1.104 7.729
GAS parameters tail
      location scale skewness shape
T+95   0.02707 2.411    0.979 4.496
T+96   0.02707 2.425    0.979 4.496
T+97   0.02707 2.386    0.979 4.496
T+98   0.02707 2.300    0.979 4.496
T+99   0.02707 2.269    0.979 4.496
T+100  0.02707 2.189    0.979 4.496


GAS rolling estimation asset 23 
GAS parameters mean
location    scale skewness    shape 
  0.1256   2.0336   1.0798   7.4246 
GAS parameters std
location    scale skewness    shape 
 0.06923  0.82152  0.01532  1.28985 
GAS parameters head
    location scale skewness shape
T+1   0.1976 2.467     1.04 7.531
T+2   0.1976 2.340     1.04 7.531
T+3   0.1976 2.298     1.04 7.531
T+4   0.1976 2.491     1.04 7.531
T+5   0.1976 2.393     1.04 7.531
T+6   0.1976 2.511     1.04 7.531
GAS parameters tail
      location scale skewness shape
T+95   0.01997 4.276    1.078 5.438
T+96   0.01997 4.059    1.078 5.438
T+97   0.01997 3.944    1.078 5.438
T+98   0.01997 3.871    1.078 5.438
T+99   0.01997 3.836    1.078 5.438
T+100  0.01997 3.925    1.078 5.438


GAS rolling estimation asset 24 
GAS parameters mean
location    scale skewness    shape 
 0.08436  1.83193  1.04113  9.51185 
GAS parameters std
location    scale skewness    shape 
 0.04714  0.59980  0.01687  2.03111 
GAS parameters head
    location scale skewness shape
T+1   0.1075 1.861    1.043 7.811
T+2   0.1075 1.967    1.043 7.811
T+3   0.1075 2.126    1.043 7.811
T+4   0.1075 2.100    1.043 7.811
T+5   0.1075 2.089    1.043 7.811
T+6   0.1075 2.144    1.043 7.811
GAS parameters tail
      location scale skewness shape
T+95  -0.00633 2.526    1.014 6.021
T+96  -0.00633 2.455    1.014 6.021
T+97  -0.00633 2.488    1.014 6.021
T+98  -0.00633 2.489    1.014 6.021
T+99  -0.00633 2.629    1.014 6.021
T+100 -0.00633 2.620    1.014 6.021


GAS rolling estimation asset 25 
GAS parameters mean
location    scale skewness    shape 
 0.08452  1.42758  1.05666  7.01862 
GAS parameters std
location    scale skewness    shape 
 0.01583  0.57522  0.01427  1.17185 
GAS parameters head
    location scale skewness shape
T+1  0.09946 1.460    1.072  6.32
T+2  0.09946 1.474    1.072  6.32
T+3  0.09946 1.465    1.072  6.32
T+4  0.09946 1.466    1.072  6.32
T+5  0.09946 1.455    1.072  6.32
T+6  0.09946 1.619    1.072  6.32
GAS parameters tail
      location scale skewness shape
T+95   0.05431 2.022    1.039 5.109
T+96   0.05431 1.971    1.039 5.109
T+97   0.05431 2.034    1.039 5.109
T+98   0.05431 1.974    1.039 5.109
T+99   0.05431 2.222    1.039 5.109
T+100  0.05431 2.297    1.039 5.109


GAS rolling estimation asset 26 
GAS parameters mean
location    scale skewness    shape 
 0.06139  1.80037  1.05294  8.21615 
GAS parameters std
location    scale skewness    shape 
 0.01870  0.71198  0.01753  0.65901 
GAS parameters head
    location scale skewness shape
T+1  0.08325 1.178     1.08 9.024
T+2  0.08325 1.209     1.08 9.024
T+3  0.08325 1.160     1.08 9.024
T+4  0.08325 1.107     1.08 9.024
T+5  0.08325 1.123     1.08 9.024
T+6  0.08325 1.097     1.08 9.024
GAS parameters tail
      location scale skewness shape
T+95   0.04326 2.889    1.039 8.058
T+96   0.04326 2.943    1.039 8.058
T+97   0.04326 2.874    1.039 8.058
T+98   0.04326 3.011    1.039 8.058
T+99   0.04326 2.940    1.039 8.058
T+100  0.04326 2.920    1.039 8.058


GAS rolling estimation asset 27 
GAS parameters mean
location    scale skewness    shape 
  0.0952   1.7513   1.0578   7.0898 
GAS parameters std
location    scale skewness    shape 
 0.01325  0.67980  0.01783  1.07256 
GAS parameters head
    location scale skewness shape
T+1  0.08755 1.526    1.081 5.333
T+2  0.08755 1.564    1.081 5.333
T+3  0.08755 1.611    1.081 5.333
T+4  0.08755 1.647    1.081 5.333
T+5  0.08755 1.644    1.081 5.333
T+6  0.08755 1.590    1.081 5.333
GAS parameters tail
      location scale skewness shape
T+95   0.07046 2.794    1.025 8.103
T+96   0.07046 2.734    1.025 8.103
T+97   0.07046 2.756    1.025 8.103
T+98   0.07046 2.868    1.025 8.103
T+99   0.07046 2.818    1.025 8.103
T+100  0.07046 2.753    1.025 8.103


GAS rolling estimation asset 28 
GAS parameters mean
location    scale skewness    shape 
 0.04608  1.75410  1.07437  8.26708 
GAS parameters std
location    scale skewness    shape 
 0.01979  0.70168  0.01768  0.65742 
GAS parameters head
    location scale skewness shape
T+1  0.06927 1.247    1.091 6.835
T+2  0.06927 1.245    1.091 6.835
T+3  0.06927 1.244    1.091 6.835
T+4  0.06927 1.244    1.091 6.835
T+5  0.06927 1.257    1.091 6.835
T+6  0.06927 1.209    1.091 6.835
GAS parameters tail
      location scale skewness shape
T+95   0.02034 2.657    1.039 8.307
T+96   0.02034 2.739    1.039 8.307
T+97   0.02034 2.786    1.039 8.307
T+98   0.02034 2.775    1.039 8.307
T+99   0.02034 2.709    1.039 8.307
T+100  0.02034 2.706    1.039 8.307


GAS rolling estimation asset 29 
GAS parameters mean
location    scale skewness    shape 
 0.05998  1.77173  1.05295 15.81272 
GAS parameters std
 location     scale  skewness     shape 
 0.029672  0.660595  0.008398 15.211726 
GAS parameters head
    location scale skewness shape
T+1  0.08139 2.047    1.047  7.68
T+2  0.08139 2.061    1.047  7.68
T+3  0.08139 1.995    1.047  7.68
T+4  0.08139 2.025    1.047  7.68
T+5  0.08139 1.956    1.047  7.68
T+6  0.08139 1.894    1.047  7.68
GAS parameters tail
      location scale skewness shape
T+95   0.01739 2.436    1.065 49.62
T+96   0.01739 2.400    1.065 49.62
T+97   0.01739 2.363    1.065 49.62
T+98   0.01739 2.349    1.065 49.62
T+99   0.01739 2.330    1.065 49.62
T+100  0.01739 2.303    1.065 49.62


GAS rolling estimation asset 30 
GAS parameters mean
location    scale skewness    shape 
 0.06681  1.56596  1.01813 10.82430 
GAS parameters std
location    scale skewness    shape 
0.009836 0.549972 0.036049 1.699063 
GAS parameters head
    location scale skewness shape
T+1  0.06059 1.302    1.047 7.528
T+2  0.06059 1.268    1.047 7.528
T+3  0.06059 1.273    1.047 7.528
T+4  0.06059 1.227    1.047 7.528
T+5  0.06059 1.192    1.047 7.528
T+6  0.06059 1.334    1.047 7.528
GAS parameters tail
      location scale skewness shape
T+95   0.07134 2.167   0.9413 11.37
T+96   0.07134 2.085   0.9413 11.37
T+97   0.07134 2.007   0.9413 11.37
T+98   0.07134 2.081   0.9413 11.37
T+99   0.07134 2.015   0.9413 11.37
T+100  0.07134 1.940   0.9413 11.37


Rolling forecast with univariate GARCH



GARCH rolling estimation asset 1 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.05738    2.30461    1.09640    7.73791    0.00000   -0.01940 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.01164    1.03037    0.02319    0.72183    0.00000    2.65111 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.07769 1.584 1.082 6.559          0   0.2083
1976-11-28 01:00:00 0.07769 1.556 1.082 6.559          0  -0.9056
1976-11-29 01:00:00 0.07769 1.541 1.082 6.559          0   0.0000
1976-11-30 01:00:00 0.07769 1.515 1.082 6.559          0   0.9056
1976-12-01 01:00:00 0.07769 1.498 1.082 6.559          0   3.3416
1976-12-02 01:00:00 0.07769 1.605 1.082 6.559          0   1.5308
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.04306 6.377 1.042 7.307          0    3.066
1985-02-08 01:00:00 0.04306 6.273 1.042 7.307          0    1.613
1985-02-09 01:00:00 0.04306 6.151 1.042 7.307          0   -3.607
1985-02-10 01:00:00 0.04306 6.066 1.042 7.307          0   -8.014
1985-02-11 01:00:00 0.04306 6.147 1.042 7.307          0   -1.292
1985-02-12 01:00:00 0.04306 6.025 1.042 7.307          0    4.451


GARCH rolling estimation asset 2 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
  0.092575   2.149066   1.066397   8.038543   0.000000  -0.001538 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.02108    1.11497    0.01564    1.07481    0.00000    2.47107 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.08068 1.871 1.069 6.035          0    0.000
1976-11-28 01:00:00 0.08068 1.811 1.069 6.035          0    2.056
1976-11-29 01:00:00 0.08068 1.828 1.069 6.035          0   -1.111
1976-11-30 01:00:00 0.08068 1.797 1.069 6.035          0    1.285
1976-12-01 01:00:00 0.08068 1.769 1.069 6.035          0    1.326
1976-12-02 01:00:00 0.08068 1.746 1.069 6.035          0   -1.326
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.05035 4.938 1.055 8.535          0   9.2915
1985-02-08 01:00:00 0.05035 5.303 1.055 8.535          0   6.7793
1985-02-09 01:00:00 0.05035 5.399 1.055 8.535          0  -6.5996
1985-02-10 01:00:00 0.05035 5.483 1.055 8.535          0   0.1196
1985-02-11 01:00:00 0.05035 5.310 1.055 8.535          0   1.4833
1985-02-12 01:00:00 0.05035 5.155 1.055 8.535          0  -5.3838


GARCH rolling estimation asset 3 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
 0.0622934  2.0331031  1.0393803  5.5538153  0.0000000 -0.0002917 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.01371    0.65899    0.02042    0.47025    0.00000    2.18978 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.06948 1.600 1.081 5.405          0  -1.8541
1976-11-28 01:00:00 0.06948 1.619 1.081 5.405          0   4.2740
1976-11-29 01:00:00 0.06948 1.855 1.081 5.405          0  -0.2301
1976-11-30 01:00:00 0.06948 1.796 1.081 5.405          0   1.8944
1976-12-01 01:00:00 0.06948 1.791 1.081 5.405          0  -0.2263
1976-12-02 01:00:00 0.06948 1.736 1.081 5.405          0   1.8633
GARCH parameters tail
                         Mu Sigma   Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.06807 3.011 0.9982 6.672          0  0.48707
1985-02-08 01:00:00 0.06807 2.929 0.9982 6.672          0  0.04626
1985-02-09 01:00:00 0.06807 2.848 0.9982 6.672          0 -6.02922
1985-02-10 01:00:00 0.06807 3.085 0.9982 6.672          0  3.85497
1985-02-11 01:00:00 0.06807 3.116 0.9982 6.672          0 -3.63414
1985-02-12 01:00:00 0.06807 3.139 0.9982 6.672          0  3.11281


GARCH rolling estimation asset 4 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.09347    2.07484    0.99080    7.70324    0.00000   -0.04251 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.02366    1.71462    0.03824    1.12340    0.00000    2.80667 
GARCH parameters head
                        Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.1153 1.689 1.059  5.35          0  0.99660
1976-11-28 01:00:00 0.1153 1.643 1.059  5.35          0 -0.05221
1976-11-29 01:00:00 0.1153 1.584 1.059  5.35          0  0.20866
1976-11-30 01:00:00 0.1153 1.528 1.059  5.35          0  2.21601
1976-12-01 01:00:00 0.1153 1.595 1.059  5.35          0  2.51649
1976-12-02 01:00:00 0.1153 1.684 1.059  5.35          0 -1.95740
GARCH parameters tail
                         Mu Sigma   Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.04257 14.39 0.9682  7.18          0    8.004
1985-02-08 01:00:00 0.04257 13.89 0.9682  7.18          0   12.833
1985-02-09 01:00:00 0.04257 13.79 0.9682  7.18          0   -8.615
1985-02-10 01:00:00 0.04257 13.37 0.9682  7.18          0   -2.994
1985-02-11 01:00:00 0.04257 12.74 0.9682  7.18          0   -9.228
1985-02-12 01:00:00 0.04257 12.45 0.9682  7.18          0  -12.405


GARCH rolling estimation asset 5 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.10403    2.28914    1.04837    7.26447    0.00000   -0.04271 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.04153    1.84651    0.02449    0.82525    0.00000    3.12522 
GARCH parameters head
                        Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.1226 2.472 1.081 5.756          0  -3.7617
1976-11-28 01:00:00 0.1226 2.580 1.081 5.756          0   3.7617
1976-11-29 01:00:00 0.1226 2.639 1.081 5.756          0   0.0000
1976-11-30 01:00:00 0.1226 2.486 1.081 5.756          0   1.5924
1976-12-01 01:00:00 0.1226 2.387 1.081 5.756          0   2.0329
1976-12-02 01:00:00 0.1226 2.327 1.081 5.756          0  -0.9331
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.02951 13.53 1.012 7.657          0    6.416
1985-02-08 01:00:00 0.02951 13.15 1.012 7.657          0   17.096
1985-02-09 01:00:00 0.02951 13.45 1.012 7.657          0   -7.411
1985-02-10 01:00:00 0.02951 13.11 1.012 7.657          0   -9.403
1985-02-11 01:00:00 0.02951 12.88 1.012 7.657          0    2.778
1985-02-12 01:00:00 0.02951 12.44 1.012 7.657          0   -5.346


GARCH rolling estimation asset 6 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.08961    2.11007    1.08258    5.64086    0.00000    0.02356 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
  0.009314   0.541744   0.030001   0.534266   0.000000   2.213334 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.07159 1.608 1.082 4.607          0  -0.8147
1976-11-28 01:00:00 0.07159 1.592 1.082 4.607          0   2.2246
1976-11-29 01:00:00 0.07159 1.614 1.082 4.607          0   0.5982
1976-11-30 01:00:00 0.07159 1.594 1.082 4.607          0   1.4474
1976-12-01 01:00:00 0.07159 1.589 1.082 4.607          0   0.1305
1976-12-02 01:00:00 0.07159 1.567 1.082 4.607          0  -1.7106
GARCH parameters tail
                        Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.0765 3.969 1.017 5.908          0  -1.0771
1985-02-08 01:00:00 0.0765 3.935 1.017 5.908          0   2.0821
1985-02-09 01:00:00 0.0765 3.907 1.017 5.908          0  -3.5470
1985-02-10 01:00:00 0.0765 3.898 1.017 5.908          0  -3.1901
1985-02-11 01:00:00 0.0765 3.885 1.017 5.908          0  -1.8319
1985-02-12 01:00:00 0.0765 3.857 1.017 5.908          0  -0.9954


GARCH rolling estimation asset 7 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.06392    1.59502    1.03078   10.18789    0.00000    0.03840 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
  0.007299   0.644425   0.032884   2.419427   0.000000   1.792775 
GARCH parameters head
                         Mu Sigma Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.06002 1.533 1.03  6.37          0  -0.7537
1976-11-28 01:00:00 0.06002 1.509 1.03  6.37          0   0.3997
1976-11-29 01:00:00 0.06002 1.479 1.03  6.37          0   1.7140
1976-11-30 01:00:00 0.06002 1.482 1.03  6.37          0  -0.5681
1976-12-01 01:00:00 0.06002 1.457 1.03  6.37          0   1.8668
1976-12-02 01:00:00 0.06002 1.468 1.03  6.37          0  -0.1722
GARCH parameters tail
                         Mu Sigma   Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.07088 2.540 0.9498 14.44          0   1.1159
1985-02-08 01:00:00 0.07088 2.454 0.9498 14.44          0   2.3308
1985-02-09 01:00:00 0.07088 2.428 0.9498 14.44          0  -4.3910
1985-02-10 01:00:00 0.07088 2.597 0.9498 14.44          0  -0.1417
1985-02-11 01:00:00 0.07088 2.494 0.9498 14.44          0  -0.3267
1985-02-12 01:00:00 0.07088 2.398 0.9498 14.44          0   1.9024


GARCH rolling estimation asset 8 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.06132    1.83007    1.07532    7.34710    0.00000   -0.01705 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.01181    0.67950    0.01372    0.52286    0.00000    1.99835 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.07163 1.730 1.053 6.464          0  -2.4962
1976-11-28 01:00:00 0.07163 1.767 1.053 6.464          0   1.8263
1976-11-29 01:00:00 0.07163 1.758 1.053 6.464          0   1.1311
1976-11-30 01:00:00 0.07163 1.726 1.053 6.464          0   1.0932
1976-12-01 01:00:00 0.07163 1.695 1.053 6.464          0   0.3534
1976-12-02 01:00:00 0.07163 1.654 1.053 6.464          0  -0.2270
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.03994 3.978 1.091  6.95          0   0.3875
1985-02-08 01:00:00 0.03994 3.906 1.091  6.95          0   6.0043
1985-02-09 01:00:00 0.03994 3.990 1.091  6.95          0  -3.8363
1985-02-10 01:00:00 0.03994 3.982 1.091  6.95          0  -3.5091
1985-02-11 01:00:00 0.03994 3.965 1.091  6.95          0  -1.3594
1985-02-12 01:00:00 0.03994 3.901 1.091  6.95          0   3.0437


GARCH rolling estimation asset 9 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.05965    1.97926    1.05542    6.18329    0.00000   -0.00184 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.01819    0.73830    0.01827    0.28053    0.00000    2.24596 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.09073 1.438 1.077 6.321          0  -0.8295
1976-11-28 01:00:00 0.09073 1.423 1.077 6.321          0   1.0129
1976-11-29 01:00:00 0.09073 1.410 1.077 6.321          0   2.1750
1976-11-30 01:00:00 0.09073 1.466 1.077 6.321          0   1.1587
1976-12-01 01:00:00 0.09073 1.455 1.077 6.321          0   1.0139
1976-12-02 01:00:00 0.09073 1.439 1.077 6.321          0   0.4813
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.03319 3.865 1.045  6.17          0    1.852
1985-02-08 01:00:00 0.03319 3.822 1.045  6.17          0    4.733
1985-02-09 01:00:00 0.03319 3.843 1.045  6.17          0   -4.733
1985-02-10 01:00:00 0.03319 3.866 1.045  6.17          0   -2.719
1985-02-11 01:00:00 0.03319 3.837 1.045  6.17          0   -2.348
1985-02-12 01:00:00 0.03319 3.803 1.045  6.17          0    2.058


GARCH rolling estimation asset 10 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
  0.084267   1.762271   1.048500   9.693465   0.000000  -0.004337 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.02265    0.83427    0.01495    1.31987    0.00000    2.03165 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.08879 1.351 1.033 8.545          0  -1.4781
1976-11-28 01:00:00 0.08879 1.361 1.033 8.545          0   2.2473
1976-11-29 01:00:00 0.08879 1.405 1.033 8.545          0   0.9153
1976-11-30 01:00:00 0.08879 1.384 1.033 8.545          0   0.7564
1976-12-01 01:00:00 0.08879 1.361 1.033 8.545          0   0.4511
1976-12-02 01:00:00 0.08879 1.333 1.033 8.545          0  -0.6775
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.03037 4.857 1.068 7.645          0    5.025
1985-02-08 01:00:00 0.03037 4.858 1.068 7.645          0    3.314
1985-02-09 01:00:00 0.03037 4.819 1.068 7.645          0   -5.951
1985-02-10 01:00:00 0.03037 4.853 1.068 7.645          0   -4.749
1985-02-11 01:00:00 0.03037 4.849 1.068 7.645          0   -4.295
1985-02-12 01:00:00 0.03037 4.833 1.068 7.645          0   -2.175


GARCH rolling estimation asset 11 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.05001    2.50035    1.10270    7.29385    0.00000   -0.07816 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.01536    1.61426    0.01630    1.33185    0.00000    3.07686 
GARCH parameters head
                         Mu Sigma Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.05466 1.602 1.09 6.287          0  -3.4215
1976-11-28 01:00:00 0.05466 1.799 1.09 6.287          0  -0.6635
1976-11-29 01:00:00 0.05466 1.750 1.09 6.287          0  -1.3049
1976-11-30 01:00:00 0.05466 1.731 1.09 6.287          0   0.8836
1976-12-01 01:00:00 0.05466 1.691 1.09 6.287          0   1.0849
1976-12-02 01:00:00 0.05466 1.662 1.09 6.287          0   0.4515
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.01288 8.289 1.069 5.356          0  -0.8915
1985-02-08 01:00:00 0.01288 8.015 1.069 5.356          0   2.0680
1985-02-09 01:00:00 0.01288 7.764 1.069 5.356          0  -7.2759
1985-02-10 01:00:00 0.01288 7.729 1.069 5.356          0  -5.4941
1985-02-11 01:00:00 0.01288 7.600 1.069 5.356          0  -4.0684
1985-02-12 01:00:00 0.01288 7.419 1.069 5.356          0  -1.3938


GARCH rolling estimation asset 12 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.10158    2.17896    1.03731    6.83212    0.00000    0.02338 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.03862    0.85937    0.01276    0.86162    0.00000    2.38537 
GARCH parameters head
                        Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.1379 1.977 1.024 7.433          0  -0.8314
1976-11-28 01:00:00 0.1379 1.936 1.024 7.433          0   1.1070
1976-11-29 01:00:00 0.1379 1.899 1.024 7.433          0   1.0949
1976-11-30 01:00:00 0.1379 1.863 1.024 7.433          0   0.2719
1976-12-01 01:00:00 0.1379 1.816 1.024 7.433          0   0.0000
1976-12-02 01:00:00 0.1379 1.773 1.024 7.433          0  -0.6355
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.01819 3.368 1.053 6.553          0  -2.7203
1985-02-08 01:00:00 0.01819 3.340 1.053 6.553          0   3.9012
1985-02-09 01:00:00 0.01819 3.362 1.053 6.553          0  -4.4452
1985-02-10 01:00:00 0.01819 3.414 1.053 6.553          0  -2.1595
1985-02-11 01:00:00 0.01819 3.367 1.053 6.553          0   0.1856
1985-02-12 01:00:00 0.01819 3.292 1.053 6.553          0   1.6096


GARCH rolling estimation asset 13 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.07994    2.51775    1.03053    5.41210    0.00000    0.02070 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.01820    0.88474    0.01213    0.36193    0.00000    2.71917 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.06488 2.449 1.005 5.688          0   1.0767
1976-11-28 01:00:00 0.06488 2.413 1.005 5.688          0   1.5182
1976-11-29 01:00:00 0.06488 2.385 1.005 5.688          0  -0.8575
1976-11-30 01:00:00 0.06488 2.350 1.005 5.688          0  -3.0867
1976-12-01 01:00:00 0.06488 2.374 1.005 5.688          0   0.6769
1976-12-02 01:00:00 0.06488 2.337 1.005 5.688          0  -2.0446
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.07232 3.439 1.016 5.016          0   0.8956
1985-02-08 01:00:00 0.07232 3.387 1.016 5.016          0   4.1479
1985-02-09 01:00:00 0.07232 3.410 1.016 5.016          0  -4.0365
1985-02-10 01:00:00 0.07232 3.434 1.016 5.016          0  -3.3393
1985-02-11 01:00:00 0.07232 3.432 1.016 5.016          0  -0.2593
1985-02-12 01:00:00 0.07232 3.379 1.016 5.016          0   4.0707


GARCH rolling estimation asset 14 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.05102    1.84253    1.03628    4.95420    0.00000    0.03494 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.02351    0.69856    0.02304    0.33449    0.00000    2.03654 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.02313 1.918 1.037 4.725          0 -0.18326
1976-11-28 01:00:00 0.02313 1.870 1.037 4.725          0  0.42709
1976-11-29 01:00:00 0.02313 1.826 1.037 4.725          0  0.78836
1976-11-30 01:00:00 0.02313 1.788 1.037 4.725          0 -1.30721
1976-12-01 01:00:00 0.02313 1.767 1.037 4.725          0  0.97443
1976-12-02 01:00:00 0.02313 1.736 1.037 4.725          0 -0.09095
GARCH parameters tail
                         Mu Sigma   Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.02806 3.184 0.9914   5.9          0  0.06548
1985-02-08 01:00:00 0.02806 3.131 0.9914   5.9          0  3.38943
1985-02-09 01:00:00 0.02806 3.137 0.9914   5.9          0 -2.46636
1985-02-10 01:00:00 0.02806 3.117 0.9914   5.9          0 -0.93398
1985-02-11 01:00:00 0.02806 3.070 0.9914   5.9          0 -0.78870
1985-02-12 01:00:00 0.02806 3.022 0.9914   5.9          0  2.76575


GARCH rolling estimation asset 15 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
  0.134116   2.648353   1.015602   7.097462   0.000000  -0.006065 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.05429    0.95118    0.01147    0.37585    0.00000    2.90577 
GARCH parameters head
                       Mu Sigma   Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.184 2.369 0.9948 6.616          0   0.3636
1976-11-28 01:00:00 0.184 2.324 0.9948 6.616          0   2.0953
1976-11-29 01:00:00 0.184 2.313 0.9948 6.616          0  -2.7629
1976-11-30 01:00:00 0.184 2.346 0.9948 6.616          0  -1.3489
1976-12-01 01:00:00 0.184 2.323 0.9948 6.616          0   0.9217
1976-12-02 01:00:00 0.184 2.285 0.9948 6.616          0  -0.6135
GARCH parameters tail
                         Mu Sigma   Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.03674 3.878 0.9918 6.923          0    3.163
1985-02-08 01:00:00 0.03674 3.859 0.9918 6.923          0    1.438
1985-02-09 01:00:00 0.03674 3.813 0.9918 6.923          0   -4.676
1985-02-10 01:00:00 0.03674 3.837 0.9918 6.923          0   -3.579
1985-02-11 01:00:00 0.03674 3.830 0.9918 6.923          0    5.505
1985-02-12 01:00:00 0.03674 3.880 0.9918 6.923          0    0.731


GARCH rolling estimation asset 16 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.07590    1.39504    1.03866    7.79875    0.00000    0.03022 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.02646    0.55083    0.01212    1.01105    0.00000    1.50503 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.09812 1.671 1.024 7.112          0  -1.7051
1976-11-28 01:00:00 0.09812 1.675 1.024 7.112          0   3.4231
1976-11-29 01:00:00 0.09812 1.804 1.024 7.112          0  -0.4580
1976-11-30 01:00:00 0.09812 1.750 1.024 7.112          0   2.5140
1976-12-01 01:00:00 0.09812 1.788 1.024 7.112          0   1.0124
1976-12-02 01:00:00 0.09812 1.744 1.024 7.112          0  -0.6062
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.03452 1.650 1.044 6.021          0   1.7355
1985-02-08 01:00:00 0.03452 1.653 1.044 6.021          0   1.7572
1985-02-09 01:00:00 0.03452 1.658 1.044 6.021          0  -0.4793
1985-02-10 01:00:00 0.03452 1.618 1.044 6.021          0  -1.0175
1985-02-11 01:00:00 0.03452 1.593 1.044 6.021          0   0.0000
1985-02-12 01:00:00 0.03452 1.550 1.044 6.021          0   1.5309


GARCH rolling estimation asset 17 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.08822    2.29440    1.03050    7.29032    0.00000    0.00175 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.02070    1.35252    0.01312    0.71644    0.00000    2.74662 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.07772 1.752 1.023 5.403          0  -0.2633
1976-11-28 01:00:00 0.07772 1.701 1.023 5.403          0   1.9579
1976-11-29 01:00:00 0.07772 1.724 1.023 5.403          0  -0.9524
1976-11-30 01:00:00 0.07772 1.694 1.023 5.403          0   3.5886
1976-12-01 01:00:00 0.07772 1.887 1.023 5.403          0   2.8544
1976-12-02 01:00:00 0.07772 1.966 1.023 5.403          0  -3.1065
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.04877 8.661 1.048 7.036          0   2.2600
1985-02-08 01:00:00 0.04877 8.423 1.048 7.036          0   9.8714
1985-02-09 01:00:00 0.04877 8.506 1.048 7.036          0  -8.4058
1985-02-10 01:00:00 0.04877 8.499 1.048 7.036          0   0.3141
1985-02-11 01:00:00 0.04877 8.249 1.048 7.036          0  -1.2227
1985-02-12 01:00:00 0.04877 8.013 1.048 7.036          0  -4.6709


GARCH rolling estimation asset 18 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.07594    2.25583    1.07303    7.23778    0.00000   -0.10707 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.02175    2.87498    0.01748    0.71707    0.00000    3.70395 
GARCH parameters head
                        Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.0795 1.332 1.059 6.726          0   0.0000
1976-11-28 01:00:00 0.0795 1.308 1.059 6.726          0   1.2966
1976-11-29 01:00:00 0.0795 1.307 1.059 6.726          0  -0.7018
1976-11-30 01:00:00 0.0795 1.293 1.059 6.726          0   2.4168
1976-12-01 01:00:00 0.0795 1.352 1.059 6.726          0  -0.1086
1976-12-02 01:00:00 0.0795 1.327 1.059 6.726          0   0.6138
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.01742 5.727 1.028 5.953          0   6.8993
1985-02-08 01:00:00 0.01742 5.844 1.028 5.953          0   4.3485
1985-02-09 01:00:00 0.01742 5.718 1.028 5.953          0  -8.8947
1985-02-10 01:00:00 0.01742 6.086 1.028 5.953          0  -0.7782
1985-02-11 01:00:00 0.01742 5.799 1.028 5.953          0  -3.9846
1985-02-12 01:00:00 0.01742 5.654 1.028 5.953          0 -13.0053


GARCH rolling estimation asset 19 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
  0.073062   1.488628   1.060216   7.090109   0.000000  -0.003799 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.03446    0.62559    0.01561    0.89989    0.00000    1.66697 
GARCH parameters head
                       Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.124 1.435 1.054 6.864          0  -1.8921
1976-11-28 01:00:00 0.124 1.471 1.054 6.864          0   1.6653
1976-11-29 01:00:00 0.124 1.475 1.054 6.864          0   1.0473
1976-11-30 01:00:00 0.124 1.452 1.054 6.864          0  -0.6353
1976-12-01 01:00:00 0.124 1.426 1.054 6.864          0   1.0431
1976-12-02 01:00:00 0.124 1.407 1.054 6.864          0   1.4142
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.02872 2.360 1.054   5.9          0   0.6948
1985-02-08 01:00:00 0.02872 2.323 1.054   5.9          0   1.2158
1985-02-09 01:00:00 0.02872 2.293 1.054   5.9          0  -0.7093
1985-02-10 01:00:00 0.02872 2.257 1.054   5.9          0  -1.9243
1985-02-11 01:00:00 0.02872 2.247 1.054   5.9          0  -1.1300
1985-02-12 01:00:00 0.02872 2.218 1.054   5.9          0   2.5247


GARCH rolling estimation asset 20 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.05641    1.73447    1.05921    6.78896    0.00000    0.03917 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.01577    0.46018    0.02962    0.93751    0.00000    1.82559 
GARCH parameters head
                        Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.0676 1.763 1.054 7.846          0   1.7449
1976-11-28 01:00:00 0.0676 1.753 1.054 7.846          0   1.9273
1976-11-29 01:00:00 0.0676 1.752 1.054 7.846          0  -0.5316
1976-11-30 01:00:00 0.0676 1.710 1.054 7.846          0  -0.5881
1976-12-01 01:00:00 0.0676 1.671 1.054 7.846          0   0.8542
1976-12-02 01:00:00 0.0676 1.637 1.054 7.846          0  -1.1227
GARCH parameters tail
                        Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.0589 2.256 1.027 6.162          0   0.2053
1985-02-08 01:00:00 0.0589 2.217 1.027 6.162          0   1.1553
1985-02-09 01:00:00 0.0589 2.187 1.027 6.162          0  -1.8068
1985-02-10 01:00:00 0.0589 2.175 1.027 6.162          0  -0.2066
1985-02-11 01:00:00 0.0589 2.137 1.027 6.162          0  -0.2070
1985-02-12 01:00:00 0.0589 2.101 1.027 6.162          0   1.6784


GARCH rolling estimation asset 21 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.05885    1.56179    1.05715    4.99400    0.00000    0.01261 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
  0.009248   0.441189   0.014570   0.189692   0.000000   1.660173 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.07133 1.444 1.043 4.897          0  -2.7226
1976-11-28 01:00:00 0.07133 1.486 1.043 4.897          0   2.0418
1976-11-29 01:00:00 0.07133 1.496 1.043 4.897          0  -1.0876
1976-11-30 01:00:00 0.07133 1.487 1.043 4.897          0   0.5453
1976-12-01 01:00:00 0.07133 1.469 1.043 4.897          0   1.2232
1976-12-02 01:00:00 0.07133 1.461 1.043 4.897          0  -0.3966
GARCH parameters tail
                         Mu Sigma Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.04594 2.724 1.05 4.865          0   0.7996
1985-02-08 01:00:00 0.04594 2.696 1.05 4.865          0   2.6142
1985-02-09 01:00:00 0.04594 2.692 1.05 4.865          0   2.0185
1985-02-10 01:00:00 0.04594 2.678 1.05 4.865          0  -5.0038
1985-02-11 01:00:00 0.04594 2.749 1.05 4.865          0  -6.0741
1985-02-12 01:00:00 0.04594 2.861 1.05 4.865          0   1.9950


GARCH rolling estimation asset 22 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
  0.075707   1.877861   1.034948   6.394838   0.000000  -0.001424 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.03611    0.60593    0.04570    1.16127    0.00000    2.03659 
GARCH parameters head
                        Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.1157 1.898 1.081 7.483          0  -2.9584
1976-11-28 01:00:00 0.1157 1.967 1.081 7.483          0   3.4326
1976-11-29 01:00:00 0.1157 2.049 1.081 7.483          0  -1.8781
1976-11-30 01:00:00 0.1157 2.030 1.081 7.483          0   0.8001
1976-12-01 01:00:00 0.1157 1.967 1.081 7.483          0   2.5182
1976-12-02 01:00:00 0.1157 1.979 1.081 7.483          0  -1.5980
GARCH parameters tail
                         Mu Sigma   Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.01247 2.159 0.9656 4.447          0   2.0656
1985-02-08 01:00:00 0.01247 2.149 0.9656 4.447          0   1.4348
1985-02-09 01:00:00 0.01247 2.112 0.9656 4.447          0   0.5544
1985-02-10 01:00:00 0.01247 2.057 0.9656 4.447          0  -1.3568
1985-02-11 01:00:00 0.01247 2.023 0.9656 4.447          0  -0.4212
1985-02-12 01:00:00 0.01247 1.970 0.9656 4.447          0   6.1721


GARCH rolling estimation asset 23 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
    0.1253     2.0578     1.0655     7.2374     0.0000     0.0192 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.06851    0.83976    0.01396    1.19306    0.00000    2.29123 
GARCH parameters head
                        Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.1932 2.407 1.032 7.019          0  -0.3854
1976-11-28 01:00:00 0.1932 2.300 1.032 7.019          0   1.8174
1976-11-29 01:00:00 0.1932 2.252 1.032 7.019          0  -3.1779
1976-11-30 01:00:00 0.1932 2.385 1.032 7.019          0  -0.9833
1976-12-01 01:00:00 0.1932 2.301 1.032 7.019          0   3.3045
1976-12-02 01:00:00 0.1932 2.393 1.032 7.019          0  -1.6386
GARCH parameters tail
                       Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.022 4.308 1.062  5.45          0    0.170
1985-02-08 01:00:00 0.022 4.199 1.062  5.45          0    2.129
1985-02-09 01:00:00 0.022 4.120 1.062  5.45          0   -2.526
1985-02-10 01:00:00 0.022 4.055 1.062  5.45          0   -2.825
1985-02-11 01:00:00 0.022 4.003 1.062  5.45          0    4.180
1985-02-12 01:00:00 0.022 4.010 1.062  5.45          0    3.689


GARCH rolling estimation asset 24 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.08225    1.87052    1.02925    9.52308    0.00000    0.00861 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.04936    0.60749    0.01897    2.00643    0.00000    1.98265 
GARCH parameters head
                        Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.1011 1.756 1.029 7.375          0   -2.764
1976-11-28 01:00:00 0.1011 1.817 1.029 7.375          0    3.949
1976-11-29 01:00:00 0.1011 1.949 1.029 7.375          0   -1.527
1976-11-30 01:00:00 0.1011 1.931 1.029 7.375          0    1.947
1976-12-01 01:00:00 0.1011 1.923 1.029 7.375          0    2.810
1976-12-02 01:00:00 0.1011 1.959 1.029 7.375          0   -1.230
GARCH parameters tail
                         Mu Sigma   Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 -0.0197 3.434 0.9955 6.129          0    1.080
1985-02-08 01:00:00 -0.0197 3.308 0.9955 6.129          0   -2.431
1985-02-09 01:00:00 -0.0197 3.241 0.9955 6.129          0   -2.094
1985-02-10 01:00:00 -0.0197 3.161 0.9955 6.129          0   -3.637
1985-02-11 01:00:00 -0.0197 3.189 0.9955 6.129          0    2.104
1985-02-12 01:00:00 -0.0197 3.115 0.9955 6.129          0    2.061


GARCH rolling estimation asset 25 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.08189    1.49415    1.04472    6.93849    0.00000    0.02718 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.01555    0.73687    0.02012    1.11479    0.00000    1.73035 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.09233 1.386 1.056 6.079          0   -1.266
1976-11-28 01:00:00 0.09233 1.384 1.056 6.079          0    1.266
1976-11-29 01:00:00 0.09233 1.374 1.056 6.079          0   -1.139
1976-11-30 01:00:00 0.09233 1.367 1.056 6.079          0    1.222
1976-12-01 01:00:00 0.09233 1.356 1.056 6.079          0    3.459
1976-12-02 01:00:00 0.09233 1.533 1.056 6.079          0    1.406
GARCH parameters tail
                         Mu Sigma Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.05318 1.795 1.02 5.181          0  0.58371
1985-02-08 01:00:00 0.05318 1.756 1.02 5.181          0  2.57674
1985-02-09 01:00:00 0.05318 1.796 1.02 5.181          0  0.06873
1985-02-10 01:00:00 0.05318 1.753 1.02 5.181          0 -6.60282
1985-02-11 01:00:00 0.05318 2.219 1.02 5.181          0 -2.69658
1985-02-12 01:00:00 0.05318 2.242 1.02 5.181          0  1.60811


GARCH rolling estimation asset 26 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.06345    1.83699    1.04436    7.91797    0.00000    0.01082 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.02007    0.75157    0.01942    0.68719    0.00000    2.04869 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.08321 1.186 1.063 8.584          0  -1.0965
1976-11-28 01:00:00 0.08321 1.201 1.063 8.584          0   0.4400
1976-11-29 01:00:00 0.08321 1.160 1.063 8.584          0   0.0000
1976-11-30 01:00:00 0.08321 1.121 1.063 8.584          0   1.0917
1976-12-01 01:00:00 0.08321 1.132 1.063 8.584          0   0.6494
1976-12-02 01:00:00 0.08321 1.110 1.063 8.584          0  -0.4324
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.04124 2.913 1.023 8.014          0 -3.41201
1985-02-08 01:00:00 0.04124 2.934 1.023 8.014          0 -0.07716
1985-02-09 01:00:00 0.04124 2.879 1.023 8.014          0 -4.74210
1985-02-10 01:00:00 0.04124 2.970 1.023 8.014          0 -0.36489
1985-02-11 01:00:00 0.04124 2.916 1.023 8.014          0  2.16963
1985-02-12 01:00:00 0.04124 2.890 1.023 8.014          0  0.83119


GARCH rolling estimation asset 27 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.09112    1.77487    1.03488    6.80415    0.00000    0.03781 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.01317    0.77292    0.02294    0.91606    0.00000    1.97797 
GARCH parameters head
                         Mu Sigma Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.08707 1.533 1.07 5.241          0  -1.5565
1976-11-28 01:00:00 0.08707 1.537 1.07 5.241          0   2.0699
1976-11-29 01:00:00 0.08707 1.552 1.07 5.241          0   1.9652
1976-11-30 01:00:00 0.08707 1.563 1.07 5.241          0   1.4335
1976-12-01 01:00:00 0.08707 1.555 1.07 5.241          0  -0.3099
1976-12-02 01:00:00 0.08707 1.532 1.07 5.241          0   0.6805
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.06505 2.544 1.008 7.929          0   1.1643
1985-02-08 01:00:00 0.06505 2.489 1.008 7.929          0   2.8430
1985-02-09 01:00:00 0.06505 2.502 1.008 7.929          0  -3.9868
1985-02-10 01:00:00 0.06505 2.601 1.008 7.929          0  -1.4276
1985-02-11 01:00:00 0.06505 2.554 1.008 7.929          0  -0.9421
1985-02-12 01:00:00 0.06505 2.496 1.008 7.929          0   1.6067


GARCH rolling estimation asset 28 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.04584    1.78124    1.06014    8.21508    0.00000    0.01398 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.02043    0.72875    0.01840    0.68921    0.00000    1.94740 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.06799 1.197 1.084 6.729          0  -0.9199
1976-11-28 01:00:00 0.06799 1.191 1.084 6.729          0  -0.9284
1976-11-29 01:00:00 0.06799 1.186 1.084 6.729          0  -0.9371
1976-11-30 01:00:00 0.06799 1.182 1.084 6.729          0   1.2802
1976-12-01 01:00:00 0.06799 1.191 1.084 6.729          0   0.0000
1976-12-02 01:00:00 0.06799 1.158 1.084 6.729          0  -0.1959
GARCH parameters tail
                         Mu Sigma Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.01679 2.658 1.02 8.436          0   -3.380
1985-02-08 01:00:00 0.01679 2.700 1.02 8.436          0    3.154
1985-02-09 01:00:00 0.01679 2.724 1.02 8.436          0   -2.257
1985-02-10 01:00:00 0.01679 2.702 1.02 8.436          0   -1.198
1985-02-11 01:00:00 0.01679 2.646 1.02 8.436          0    2.382
1985-02-12 01:00:00 0.01679 2.632 1.02 8.436          0    3.122


GARCH rolling estimation asset 29 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.05730    1.78638    1.04431    8.75400    0.00000    0.04588 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.02795    0.67261    0.01052    0.90941    0.00000    1.92675 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.07485 2.134 1.038  7.35          0  -1.9239
1976-11-28 01:00:00 0.07485 2.123 1.038  7.35          0   0.5055
1976-11-29 01:00:00 0.07485 2.070 1.038  7.35          0   2.3257
1976-11-30 01:00:00 0.07485 2.075 1.038  7.35          0   0.0000
1976-12-01 01:00:00 0.07485 2.021 1.038  7.35          0   0.4097
1976-12-02 01:00:00 0.07485 1.972 1.038  7.35          0   1.3805
GARCH parameters tail
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.01188 2.359 1.062  8.57          0   0.3902
1985-02-08 01:00:00 0.01188 2.321 1.062  8.57          0  -0.1231
1985-02-09 01:00:00 0.01188 2.282 1.062  8.57          0  -1.8015
1985-02-10 01:00:00 0.01188 2.268 1.062  8.57          0  -1.5583
1985-02-11 01:00:00 0.01188 2.249 1.062  8.57          0  -1.1741
1985-02-12 01:00:00 0.01188 2.222 1.062  8.57          0   2.6278


GARCH rolling estimation asset 30 
GARCH parameters mean
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
   0.06436    1.58682    1.01039   10.64821    0.00000    0.04692 
GARCH parameters std
        Mu      Sigma       Skew      Shape Shape(GIG)   Realized 
  0.007734   0.649721   0.046608   1.644329   0.000000   1.766652 
GARCH parameters head
                         Mu Sigma  Skew Shape Shape(GIG) Realized
1976-11-27 01:00:00 0.05947 1.231 1.048 7.149          0   0.7295
1976-11-28 01:00:00 0.05947 1.207 1.048 7.149          0   1.2384
1976-11-29 01:00:00 0.05947 1.206 1.048 7.149          0  -0.3596
1976-11-30 01:00:00 0.05947 1.177 1.048 7.149          0  -0.5160
1976-12-01 01:00:00 0.05947 1.153 1.048 7.149          0   2.6042
1976-12-02 01:00:00 0.05947 1.271 1.048 7.149          0  -0.2523
GARCH parameters tail
                         Mu Sigma   Skew Shape Shape(GIG) Realized
1985-02-07 01:00:00 0.06192 2.312 0.9196 11.04          0   0.4063
1985-02-08 01:00:00 0.06192 2.235 0.9196 11.04          0   0.4173
1985-02-09 01:00:00 0.06192 2.161 0.9196 11.04          0  -2.8802
1985-02-10 01:00:00 0.06192 2.209 0.9196 11.04          0  -0.6776
1985-02-11 01:00:00 0.06192 2.142 0.9196 11.04          0   0.2742
1985-02-12 01:00:00 0.06192 2.071 0.9196 11.04          0   1.8475


MULTIVARIATE FORECAST
---------------------



UNIVARIATE COMPARISON
---------------------

[[1]]
 [1] "rugarch"   "parallel"  "GAS"       "stats"     "graphics"  "grDevices" "utils"     "datasets"  "methods"  
[10] "base"     

[[2]]
 [1] "rugarch"   "parallel"  "GAS"       "stats"     "graphics"  "grDevices" "utils"     "datasets"  "methods"  
[10] "base"     

[[3]]
 [1] "rugarch"   "parallel"  "GAS"       "stats"     "graphics"  "grDevices" "utils"     "datasets"  "methods"  
[10] "base"     

[[4]]
 [1] "rugarch"   "parallel"  "GAS"       "stats"     "graphics"  "grDevices" "utils"     "datasets"  "methods"  
[10] "base"     



MULTIVARIATE COMPARISON
-----------------------



TABLES
------



Table 3
     NLS           uniform       center        tails         tail_r        tail_l            
AA   "$-1.98^b$"   "$-2.36^a$"   "$-2.15^b$"   "$-2.02^b$"   "$-2.16^b$"   "$-1.04^{~}$ \\\\"
AXP  "$-2.98^a$"   "$-2.35^a$"   "$-3.14^a$"   "$-1.21^{~}$" "$-1.53^c$"   "$-1.60^c$ \\\\"  
BA   "$-1.44^c$"   "$-1.91^b$"   "$-2.79^a$"   "$-1.13^{~}$" "$-1.21^{~}$" "$-1.39^c$ \\\\"  
BAC  "$-2.95^a$"   "$-1.44^c$"   "$-3.80^a$"   "$ 0.22^{~}$" "$ 1.26^{~}$" "$-4.00^a$ \\\\"  
C    "$-0.66^{~}$" "$-0.55^{~}$" "$-1.82^b$"   "$ 0.34^{~}$" "$-1.59^c$"   "$ 0.40^{~}$ \\\\"
CAT  "$-5.26^a$"   "$-5.20^a$"   "$-5.61^a$"   "$-3.77^a$"   "$-2.17^b$"   "$-5.30^a$ \\\\"  
CVX  "$ 0.84^{~}$" "$ 1.26^{~}$" "$ 0.00^{~}$" "$ 1.41^c$"   "$ 0.71^{~}$" "$ 1.04^{~}$ \\\\"
DD   "$-1.08^{~}$" "$-0.57^{~}$" "$-0.53^{~}$" "$-0.51^{~}$" "$ 0.23^{~}$" "$-0.91^{~}$ \\\\"
DIS  "$-2.10^b$"   "$-1.69^b$"   "$-2.40^a$"   "$-1.00^{~}$" "$-1.69^b$"   "$-0.84^{~}$ \\\\"
GE   "$-3.29^a$"   "$-3.33^a$"   "$-3.76^a$"   "$-2.61^a$"   "$-3.44^a$"   "$-2.21^b$ \\\\"  
GM   "$ 0.08^{~}$" "$-0.42^{~}$" "$-1.22^{~}$" "$-0.20^{~}$" "$-1.04^{~}$" "$ 0.39^{~}$ \\\\"
HD   "$-3.39^a$"   "$-2.53^a$"   "$-1.84^b$"   "$-2.72^a$"   "$-1.44^c$"   "$-1.91^b$ \\\\"  
HPQ  "$-4.25^a$"   "$-4.50^a$"   "$-3.58^a$"   "$-4.53^a$"   "$-3.08^a$"   "$-3.50^a$ \\\\"  
IBM  "$-3.54^a$"   "$-3.79^a$"   "$-3.41^a$"   "$-3.57^a$"   "$-1.99^b$"   "$-3.47^a$ \\\\"  
INTC "$-3.17^a$"   "$-1.71^b$"   "$-1.70^b$"   "$-1.38^c$"   "$-2.93^a$"   "$ 0.09^{~}$ \\\\"
JNJ  "$-3.74^a$"   "$-2.15^b$"   "$-3.57^a$"   "$-0.69^{~}$" "$-0.14^{~}$" "$-3.05^a$ \\\\"  
JPM  "$-2.05^b$"   "$-2.12^b$"   "$-2.91^a$"   "$-1.21^{~}$" "$-1.22^{~}$" "$-1.55^c$ \\\\"  
AIG  "$ 1.07^{~}$" "$ 0.66^{~}$" "$-1.10^{~}$" "$ 0.71^{~}$" "$-0.79^{~}$" "$ 0.96^{~}$ \\\\"
KO   "$-3.12^a$"   "$-3.07^a$"   "$-3.78^a$"   "$-1.59^c$"   "$-3.39^a$"   "$-1.69^b$ \\\\"  
MCD  "$-2.03^b$"   "$-1.86^b$"   "$-2.21^b$"   "$-1.39^c$"   "$-1.67^b$"   "$-1.10^{~}$ \\\\"
MMM  "$-4.15^a$"   "$-4.54^a$"   "$-4.13^a$"   "$-4.12^a$"   "$-3.33^a$"   "$-3.37^a$ \\\\"  
MRK  "$-2.98^a$"   "$-3.63^a$"   "$-4.15^a$"   "$-3.08^a$"   "$-4.56^a$"   "$-1.91^b$ \\\\"  
MSFT "$-3.42^a$"   "$-2.74^a$"   "$-3.14^a$"   "$-1.64^c$"   "$-2.64^a$"   "$-1.69^b$ \\\\"  
PFE  "$-3.65^a$"   "$-3.54^a$"   "$-3.72^a$"   "$-3.07^a$"   "$-4.03^a$"   "$-2.46^a$ \\\\"  
PG   "$-1.78^b$"   "$-1.85^b$"   "$-2.91^a$"   "$-1.25^{~}$" "$-1.34^c$"   "$-1.31^c$ \\\\"  
T    "$-0.41^{~}$" "$-0.24^{~}$" "$-1.19^{~}$" "$ 0.26^{~}$" "$ 0.35^{~}$" "$-0.65^{~}$ \\\\"
UTX  "$-1.50^c$"   "$-1.61^c$"   "$-1.74^b$"   "$-1.38^c$"   "$-1.10^{~}$" "$-0.89^{~}$ \\\\"
VZ   "$-1.99^b$"   "$-1.94^b$"   "$-1.50^c$"   "$-1.95^b$"   "$-1.35^c$"   "$-1.52^c$ \\\\"  
WMT  "$ 2.11^b$"   "$ 0.92^{~}$" "$ 0.84^{~}$" "$ 0.81^{~}$" "$-0.42^{~}$" "$ 1.68^b$ \\\\"  
XOM  "$ 0.15^{~}$" "$ 0.38^{~}$" "$-1.29^c$"   "$ 0.72^{~}$" "$ 0.69^{~}$" "$-0.04^{~}$ \\\\"
      test     pvalue 
-3.3420174  0.0004159 


FIGURES
-------



Figure 1
null device 
          1 
